Finiteness properties for totally disconnected locally compact groups

In recent decades, geometric group theory has been extended to the setting of locally compact groups. However, in this broader context, many tools from the discrete theory do not apply directly, and more sophisticated techniques are required. A central theme of my research is the study of finiteness properties, such as being of type Fₙ, type FPₙ, and having finite cohomological dimension. In this talk, I will briefly introduce these finiteness properties, with particular emphasis on the class of totally disconnected locally compact groups, and explain why these properties are of interest. The goal is to outline the recent progress in this emerging area of research and to highlight the main obstacles encountered when extending results from the discrete to the topological setting.

The seminar “Finiteness properties for totally disconnected locally compact groups” by Ilaria Castellano researcher of Department of Mathematical Sciences "Giuseppe Luigi Lagrange"-DISMA will take place on Tuesday, 14 October 2025, at 10:00 a.m., in Aula Buzano.